Supermathematics and its Applications in Statistical Physics

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Synopsis
This text presents the mathematical concepts of Grassmannvariables and the method of supersymmetry to a broad audience of physicistsinterested in applying these tools to disordered and critical systems, as wellas related topics in statistical physics. Based on many courses and seminarsheld by the author, one of the pioneers in this field, the reader is given asystematic and tutorial introduction to the subject matter. The algebra and analysis of Grassmann variables ispresented in part I. The mathematics of these variables is applied to a randommatrix model, path integrals for fermions, dimer models and the Ising model intwo dimensions. Supermathematics - the use of commuting and anticommutingvariables on an equal footing - is the subject of part II. The properties ofsupervectors and supermatrices, which contain both commuting and Grassmanncomponents, are treated in great detail, including the derivation of integraltheorems. In part III, supersymmetric physical models are considered. Whilesupersymmetry was first introduced in elementary particle physics as exactsymmetry between bosons and fermions, the formal introduction of anticommutingspacetime components, can be extended to problems of statistical physics, and,since it connects states with equal energies, has also found its way intoquantum mechanics. Several models are considered in the applications, afterwhich the representation of the random matrix model by the nonlinearsigma-model, the determination of the density of states and the levelcorrelation are derived. Eventually, the mobility edge behavior is discussedand a short account of the ten symmetry classes of disorder, two-dimensionaldisordered models, and superbosonization is given.
Copyright:
2016

Book Details

Book Quality:
Publisher Quality
ISBN-13:
9783662491706
Publisher:
Springer Berlin Heidelberg, Berlin, Heidelberg
Date of Addition:
Copyrighted By:
Springer
Adult content:
No
Language:
English
Has Image Descriptions:
No
Categories:
Nonfiction, Science, Earth Sciences, Mathematics and Statistics
Submitted By:
Bookshare Staff
Usage Restrictions:
This is a copyrighted book.

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